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## Objective / Aim of the Experiment

To find the low resistance by Carey Fosters Bridge Experiment Setup

### Apparatus Required

Low Resistance

DC Power Supply (2V)

Carey Fosters Bridge Setup

Galvanometer

One way key

### Formula Used

X = (d_{2}Y_{1} - d_{1}Y_{2}) / (d_{2}-d_{1})

### Circuit Diagram of Carey Foster Bridge Experiment

### Theory

Carey Fosters bridge is a modified Wheatstone bridge. Here a potentiometer wire MN is inserted between the R and S arms of the Wheatstone bridge as shown in Figure above. The ratio arms P & Q are made equal. Gap 1 carries a small resistance (known) and the Gap 2 (fourth arm) carries the unknown resistance. If ρ be the resistance per unit length of wire, r_{1} & r_{2} be the end resistances at M & N, MD = l_{1} is balancing length a shown in figure.

then P / Q = (X + l_{1}ρ + r_{1}) / [Y + (100-l_{1})ρ + r_{2}] ............. (1)

When, X & Y are interchanged, the balance point shifts to a length _{2}, then,

then P / Q = (Y + l_{2}ρ + r_{1}) / [X + (100-l_{2})ρ + r_{2}] ............. (2)

Comparing (1) & (2) and adding 1 to both sides, we get,

Y - X = (l_{1} - l_{2})ρ

Where X is unknown resistance, (l_{1} - l_{2}) is shift in balance point when the positions of X & Y are interchanged. Let d_{1} & d_{2} are the shifts corresponding to resistances Y_{1} & Y_{2}, then,

X - Y_{1} = d_{1}ρ and X - Y_{2} = d_{2}ρ, so, (X - Y_{1}) / (X - Y_{2}) = d_{1} / d_{2}

X = (d_{2}Y_{1} - d_{1}Y_{2}) / (d_{2}-d_{1})

### Procedure

1. Make connection as shown in the figure.

2. Fix P = Q = 1 Ω throughout the experiment.

3. Keep X = Y = 0 by short circuiting by copper plates to get balance point.

4. Repeat step (iii) by interchanging the position of copper plates and determine x 0 .

5. Replace trip of gap 1 by unknown resistance X and gap 2 by known resistance Y. Find balance point for 0.1 Ω, and, then interchange X & Y, and, again find balance point.

6. Repeat this step for Y = 0.2, 0.3, 0.4, 0.5 Ω.

### Observations

(a) Determination of electrical zero:

(a) Determination of unknown resistance:

### Result

The value of unknown resistance is .............. Ω.

### Precautions

- All terminals should be tight.
- The connecting wires and the copper strip should be thoroughly cleaned with sand paper.
- The connection should be tight and the plugs of the resistance box should be given twist so that they are tight.
- The battery key should be taken out when the readings is not being taken in order to avoid heating and the wire.

### Carey Fosters Bridge Viva Questions and Answers

Question-1: What do you mean by the resistance of a conductor?

Answer-1: The ratio of the potential difference between the two ends of a conductor to the current flowing in it, is called the resistance of a conductor.

Question-2: On what factor does it depends?

Answer-2: Resistancve of a conductor is directly proportional yo its length(l), inversely proportional to the area of cross section (A). It also depends upon the nature of material and temperature of the conductor.

Question-3: What is its unit?

Answer-3: Unit if resistance is ohm.

Question-4: What is effect of temperature on resistance?

Answer-4: It increases with the increase in temperature.

Question-5: What is the effect of increasing the effective length of a Carey Fosters bridge wire?

Answer-5: It will increase the accuracy of the result because then percentage error in reading the position of the balance point is very much decreased.

Question-6: What is the minimum difference in resistance that you can measure with this bridge wire?

Answer-6: It is equal to the resistance of the one millimeter length of the bridge wire.

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